If R is a relation from a finite set A having | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) relation $R$ from set $A$ to set $B$ is defined as a subset of the Cartesian product $A 	imes B$.Given that set $A$ has $m$ elements and set $B$

Vedclass · Accepted Answer

$2^{mn}$

Vedclass · Answer

(A) relation $R$ from set $A$ to set $B$ is defined as a subset of the Cartesian product $A 	imes B$.Given that set $A$ has $m$ elements and set $B$ has $n$ elements,the number of elements in the Cartesian product $A 	imes B$ is $|A 	imes B| = |A| 	imes |B| = m 	imes n = mn$.The total number of subsets of a set with $k$ elements is $2^k$.Since a relation is any subset of $A 	imes B$,the total number of relations from $A$ to $B$ is the number of subsets of $A 	imes B$.Therefore,the number of relations is $2^{mn}$.

If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements,then the number of relations from $A$ to $B$ is:

Similar Questions

Let $R$ be a relation in the set of natural numbers $N$ defined by $R = \{(a, b) : a = b - 2, b > 6\}$. Which of the following is correct?

If $R=\{(x, y): x, y \in Z, x^{2}+3 y^{2} \leq 8\}$ is a relation on the set of integers $Z,$ then the domain of $R^{-1}$ is

The figure shows a relation between the sets $P$ and $Q$. Write this relation in set-builder form. What are its domain and range?

Two finite sets $A$ and $B$ are such that $n(A) = 2$ and $n(B) = 3$. Then the total number of relations from $A$ to $B$ is:

Let $X = \{ 1, 2, 3, 4, 5 \}$ and $Y = \{ 1, 3, 5, 7, 9 \}$. Which of the following is/are relations from $X$ to $Y$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module